no. 2
PSL(2,7) septimic fields with a power basis
Lavallee, Melisa J.1 ; Spearman, Blair K.1 ; Yang, Qiduan1
1 Department of Mathematics and Statistics University of British Columbia Okanagan Kelowna, BC, Canada, V1V 1V7
Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 369-375

We give an infinite set of distinct monogenic septimic fields whose normal closure has Galois group PSL(2,7).

Nous donnons un ensemble infini de corps de degré 7 monogènes distincts dont la clôture normale a pour groupe de Galois PSL(2,7).

DOI : 10.5802/jtnb.801
Classification : 11R04, 11R32
Keywords: Galois Group, Septimic Field, Power Basis

Lavallee, Melisa J. 1 ; Spearman, Blair K. 1 ; Yang, Qiduan 1

1 Department of Mathematics and Statistics University of British Columbia Okanagan Kelowna, BC, Canada, V1V 1V7 
@article{JTNB_2012__24_2_369_0,
     author = {Lavallee, Melisa J. and Spearman, Blair K. and Yang, Qiduan},
     title = {PSL$(2,7)$ septimic fields with a power basis},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {369--375},
     year = {2012},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {24},
     number = {2},
     doi = {10.5802/jtnb.801},
     zbl = {1280.11062},
     mrnumber = {2950697},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/jtnb.801/}
}
TY  - JOUR
AU  - Lavallee, Melisa J.
AU  - Spearman, Blair K.
AU  - Yang, Qiduan
TI  - PSL$(2,7)$ septimic fields with a power basis
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2012
SP  - 369
EP  - 375
VL  - 24
IS  - 2
PB  - Société Arithmétique de Bordeaux
UR  - https://www.numdam.org/articles/10.5802/jtnb.801/
DO  - 10.5802/jtnb.801
LA  - en
ID  - JTNB_2012__24_2_369_0
ER  - 
%0 Journal Article
%A Lavallee, Melisa J.
%A Spearman, Blair K.
%A Yang, Qiduan
%T PSL$(2,7)$ septimic fields with a power basis
%J Journal de théorie des nombres de Bordeaux
%D 2012
%P 369-375
%V 24
%N 2
%I Société Arithmétique de Bordeaux
%U https://www.numdam.org/articles/10.5802/jtnb.801/
%R 10.5802/jtnb.801
%G en
%F JTNB_2012__24_2_369_0
Lavallee, Melisa J.; Spearman, Blair K.; Yang, Qiduan. PSL$(2,7)$ septimic fields with a power basis. Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 369-375. doi: 10.5802/jtnb.801

[1] H. Cohen, A Course in Computational Algebraic Number Theory. Springer-Verlag, 2000. | Zbl | MR

[2] I. Gaál, Diophantine equations and power integral bases. New Computational Methods. Birkhauser, Boston, 2002. | MR | Zbl

[3] M.-N. Gras, Non-monogénéité de l’anneau des entiers des extensions cycliques de Q de degré premier l≥5. J. Number Theory 23 (1986), 347–353. | Zbl | MR

[4] C. U. Jensen, A. Ledet, N. Yui, Generic Polynomials, constructive aspects of Galois theory, MSRI Publications. Cambridge University Press, 2002. | MR | Zbl

[5] M. J. Lavallee, B. K. Spearman, K. S. Williams, and Q. Yang, Dihedral quintic fields with a power basis. Mathematical Journal of Okayama University, vol. 47 (2005), 75–79. | MR | Zbl

[6] Y. Motoda, T. Nakahara and K. H Park, On power integral bases of the 2-elementary abelian extension fields. Trends in Mathematics, Information Center for Mathematical Sciences, Volume 8 (June 2006), Number 1, 55–63.

[7] M. Nair, Power free values of polynomials. Mathematika 23 (1976), 159–183. | Zbl | MR

[8] B. K. Spearman, A. Watanabe and K. S. Williams, PSL(2,5) sextic fields with a power basis. Kodai Math. J., Vol. 29 (2006), No. 1, 5–12. | MR | Zbl

[9] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers. Third Edition, Springer, 2000. | Zbl | MR

Cité par Sources :